Nanomechanical and micromechanical oscillators have been explored to enable ultrasensitive mass and/or force detection for use in chemical and biological sensing. Known nanomechanical and micromechanical oscillators have cantilevers, similar to microfabricated cantilevers used in atomic force microscopy (AFM). These cantilevers are driven to oscillate in a linear regime to detect small changes in mass and/or force by measuring changes in a resonance frequency of the cantilevers.
In recent years, a series of nanomechanical oscillators have been developed that are capable of detecting femtogram (10−15 g), attogram (10−18 g) and zeptogram (10−21 g) levels of sensitivity. Theoretically, if all noise except thermal noise is removed from a system, a fundamental limit of an appropriately designed nanomechanical oscillator can approach one atomic mass unit (approximately 1.66×10−24 g). However, experimentally achievable results of known nanomechanical oscillators are comprised by multiple sources of noise and energy dissipation in addition to thermal noise.
Energy dissipation and thermal noise both tend to randomize a motion of the cantilevers in a manner similar to Brownian motion. As a result, known nanomechanical and micromechanical oscillators are characterized by a relatively wide bell shaped, Lorentizan, resonating curve with uncertainty of a center position in a range of 10−3 to 10−5 g. This limits how small of a mass, compared to a mass of the nanomechanical and micromechanical oscillators, can be measured. For example, in order to detect a femtogram (10−15 g) level mass change, known nanomechanical and micromechanical oscillators must be smaller than a few micrometers and capable of resonating in a radio frequency range.
In addition to noise, known nanomechanical and micromechanical oscillators are limited by difficulties associated with accurately measuring the resonance frequency of the oscillators. Known nanomechanical and micromechanical oscillators and known methods of detecting mass or force rely on detecting changes in a resonance frequency of the structure, which can be closely approximated by a harmonic, i.e. linear, oscillator. Because the known methods rely on detecting changes in the resonance frequency, they are limited to oscillation amplitudes in the linear regime and thus are limited to a maximum amplitude that is below the nonlinearity onset. This translates into a challenging task of measuring and analyzing oscillation amplitudes as small as 10−10 m, about the size of a hydrogen atom. Such measurements require the use of sophisticated low-noise optical and electronic components, such as position sensitive detectors, lock-in amplifiers and phased locked loops. These technical challenges of measuring small oscillation amplitudes impede practical applications of such devices.
Other known methods of using nanomechanical and micromechanical oscillators achieve improved stability by exciting large oscillation amplitudes to minimize effects of thermal and ambient noise. However, these known nanomechanical and micromechanical oscillators become nonlinear at large oscillations and the resonance behavior cannot be analyzed using known methods and instruments for linear resonators. In particular, mass loading of nanomechanical and micromechanical oscillators cannot be determined by fitting a resonance curve of the oscillator to a Lorentzian curve or by measuring an output frequency of a self-oscillating circuitry based on a phased-locked loop.